Problem: What do the following two equations represent? $-x-5y = 1$ $2x+10y = -5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-x-5y = 1$ $-5y = x+1$ $y = -\dfrac{1}{5}x - \dfrac{1}{5}$ Putting the second equation in $y = mx + b$ form gives: $2x+10y = -5$ $10y = -2x-5$ $y = -\dfrac{1}{5}x - \dfrac{1}{2}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.